A DELAYED PREDATOR-PREY MODEL WITH PREY POPULATION GUIDED ANTI-PREDATOR BEHAVIOUR AND STAGE STRUCTURE

Lingshu Wang; Mei Zhang; Meizhi Jia

doi:10.11948/20200212

2021 Volume 11 Issue 4

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Lingshu Wang, Mei Zhang, Meizhi Jia. A DELAYED PREDATOR-PREY MODEL WITH PREY POPULATION GUIDED ANTI-PREDATOR BEHAVIOUR AND STAGE STRUCTURE[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1811-1824. doi: 10.11948/20200212

Citation:

Lingshu Wang, Mei Zhang, Meizhi Jia. A DELAYED PREDATOR-PREY MODEL WITH PREY POPULATION GUIDED ANTI-PREDATOR BEHAVIOUR AND STAGE STRUCTURE[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1811-1824. doi: 10.11948/20200212

A DELAYED PREDATOR-PREY MODEL WITH PREY POPULATION GUIDED ANTI-PREDATOR BEHAVIOUR AND STAGE STRUCTURE

1.
School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, China

Corresponding author: Email: wanglingshu@126.com(L. Wang)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 11626080), the Natural Science Foundation of Hebei Province (No. A2019207070), the Scientific Research Foundation of Hebei Education Department (No. ZD2018052) and the Foundation of Hebei University of Economics and Business(NO. 2021ZD07)

Abstract

Abstract

We consider a predator-prey model with stage structure for the prey and anti-predator behaviour such that the adult prey can attack vulnerable predators. In which a time delay due to the gestation of the predator is incorporated into this model. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the positive equilibrium are established, respectively. By using Lyapunov functionals and LaSalleӳ invariance principle, sufficient conditions are obtained for the global stability of the trivial equilibrium, the predatorextinction equilibrium and the positive equilibrium, respectively. Numerical simulations are performed to illustrate the theoretical results.
- Predator-prey model /
- anti-predator behaviour /
- stage structure /
- time delay /
- Hopf bifurcation /
- stability
MSC: 34K18, 34K20, 34K60, 92D25

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References

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